Given $ m \angle LOM = 9x + 13$, $ m \angle MON = 5x + 12$, and $ m \angle LON = 39$, find $m\angle MON$. $O$ $L$ $N$ $M$
From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {9x + 13} + {5x + 12} = {39}$ Combine like terms: $ 14x + 25 = 39$ Subtract $25$ from both sides: $ 14x = 14$ Divide both sides by $14$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 5({1}) + 12$ Simplify: $ {m\angle MON = 5 + 12}$ So ${m\angle MON = 17}$.